Shumpert would be moved to the Rockets for primarily a package of non-guaranteed contracts, which would allow Cleveland to create financial flexibility to pursue other roster upgrades.
Shumpert has two years and $21.3 million left on his contract.
His second year is a player option, which he has refused to waive in Cleveland's trade discussions with other teams about acquiring him.
It would be the second time the 27-year-old shooting guard has been traded as the New York Knicks dealt Shumpert to the Cavs during the 2014-15 season.
Shumpert played for Rockets coach Mike D'Antoni while with the Knicks.
By trading Shumpert, the committed salaries in Cleveland would drop from $125 million to $115 million guaranteed, $4 million below the luxury tax, and save the team $17.1 million in potential taxes.
In total, the trade could save the Cavaliers $28 million this season, factoring in Shumpert's contract and tax savings.
Shumpert averaged 7.5 points, 2.9 rebounds and 1.4 assists while playing a career-high 76 regular season games in Cleveland last season.
Information from ESPN's Bobby Marks was used in this report.